First Quantisation for Physics in Strong Fields

24 Feb 2025, 09:00 → 27 Feb 2025, 17:30 Europe/London

Higgs Centre Seminar Room (4305) (James Clerk Maxwell Building )

Overview

First quantised, or worldline, approaches to QFT are growing in popularity, not least due to recent successes in the areas of QFT in strong fields, and in the amplitudes-based approach to the classical 2-body problem in gravitation. Moreover, the worldline formalism has a long history of providing non-perturbative information on processes in both QED and QCD, including at finite temperature. It is now recognised as a powerful alternative to the standard "field-theoretic" approach, especially for high-multiplicity processes.

 

The aim of this Higgs Centre workshop is to bring members of different communities together to exchange ideas on worldline approaches to strong field physics, scattering amplitudes for classical gravity, and real-time path-integrals for cosmology. It will provide a forum to stimulate new collaborations and knowledge exchange between different groups using first quantisation.

Format

This three and a half day workshop will include talks and extended discussion sessions in order to facilitate cross-disciplinary interactions.

 

Lunch and refreshments will be provided. There are limited funds available to support ECRs who would not otherwise be able to attend.

Organizers

• Patrick Copinger, University of Plymouth, UK
• James P. Edwards, University of Plymouth, UK
• Anton Ilderton, University of Edinburgh, UK
• Karthik Rajeev, University of Edinburgh, UK

 

Practical information

The conference will take place in the Higgs Centre seminar room 4305, on the 4th floor of the James Clerk Maxwell building ("JCMB"), on the Kings Buildings Campus, click this link for a map of the campus area.

From the main entrance to JCMB, take the stairs or lift to floor 4, and follow signs to 4305.

For thos staying in the KM hotel/apartments, it is roughly a 35 minute walk to JCMB.
For public transport from KM, walk to the Chapel Street bus stop and take the  Number 9 bus (direction "Kings Buildings") which stops on campus, or the Number 12 bus (direction "Portobello"), and alight at "Rankin Drive", which is directly next to campus.

For those staying elsewhere in Old Town, the 9 and 12 busses are also the quickest way to the venue.

Privacy notice.docx

Monday 24 February

13:15 → 13:30 Opening remarks

Conveners: Anton Ilderton (UoE), James Edwards (University of Plymouth)

Opening.pdf

13:30 → 14:15 Talk

Convener: James Edwards (University of Plymouth)

13:30 Unified Worldline treatment of a Dirac particle with (pseudo)scalar and (axial)vector couplings

We present a worldline representation of the one-loop effective action for a Dirac particle coupled to external scalar, pseudoscalar, vector and axialvector fields, which allows one to treat the real and the imaginary parts of the effective action in a unified manner, at the price of having a non-Hermitian Hamiltonian. Unlike other existing worldline representations, our new worldline action contains terms with an odd number of Grassmann fields, leading to ordering problems that in the worldline formalism are usually encountered only in curved space, and which we treat employing the Time Slicing regularisation of the path integral with its specific “counterterm Lagrangian”, which we calculate non-perturbatively, to provide unambiguous rules to treat products of distributions occurring in some diagrams of the one-dimensional worldline theory. We then employ the usual worldline machinery to lay out the rules for the calculation of the effective action itself as well as the corresponding one-loop amplitudes. We discuss possible applications of our representation in the computation of higher-loop corrections for the Heisenberg-Euler Lagrangians, as well as the calculation of pair-creation rates of various particles, in the presence of strong external fields.

Speaker: Olindo Corradini (Università di Modena e Reggio Emilia)

Edinburgh25-WL_OC.pdf

14:15 → 15:00 Talk

Convener: James Edwards (University of Plymouth)

14:15 Low-energy master formulae on the loop and line in a homogeneous electromagnetic field

An $N-$photon dressed propagator in (s)QED at tree level and effective action to one-loop in an arbitrary homogeneous electromagnetic field are examined in a photon low-energy limit. On the line, in a Fock-Schwinger gauge for the $N-$photons, it is discussed how the photons resemble a superposition of homogeneous fields, in addition to the background field. On the loop and on the line, in both coordinate and momentum representations, an expansion of the photons is demonstrated in terms of worldline Green functions in a background homogeneous field. We further discuss a recursion relation to treat the expansion, complimentary to the Green function approach.

Speaker: Patrick Copinger (University of Plymouth)

Copinger.pdf

15:00 → 15:30 Coffee Break

15:30 → 17:00 Discussions

Tuesday 25 February

09:15 → 10:00 Talk

Convener: Anton Ilderton (UoE)

09:15 The Worldline Formalism and the Gauge/Gravity Correspondence

The worldline formalism is a powerful tool to explore the strong coupling regime of QCD. Together with the AdS/CFT correspondence it leads to powerful results, in particular about meson correlators and meson scattering.
Another application of the worldline formalism that I hope to report is the relation between 2d QCD and the string worldsheet.

Speaker: Adi Armoni (Swansea University)

Talk_in_Higgs_centre.pdf

10:00 → 10:45 Talk

Convener: Anton Ilderton (UoE)

10:00 Magnetic monopole pair production in strong magnetic fields

If magnetic monopoles exist, they are produced in strong magnetic fields by the electromagnetic dual of the Schwinger pair creation process. This phenomenon can be described non-perturbatively using the worldline instanton approach, and therefore it avoids the problems the strength of the magnetic charge required by the Dirac quantisation condition poses to any perturbative calculations. I present a calculation of the production probability of monopoles for ultraperipheral heavy-ion collisions at the LHC, and the monopole mass bounds obtained by the MoEDAL experiment based on it.

Speaker: Arttu Rajantie (Imperial College London)

rajantie_edinburgh_2025b.pdf

10:45 → 11:15 Coffee Break

11:15 → 12:45 Discussions

13:45 → 14:30 Talk

Convener: Patrick Copinger (University of Plymouth)

13:45 Worldline instantons for the momentum spectrum of strong-field-QED processes in space-time dependent fields

Affleck et al used worldline instantons to obtain an all-orders-in-$\alpha$ result for Schwinger pair production by a constant electric field.
Dunne and Schubert et al showed how to use instantons to obtain the probability for non-constant fields.
In both cases, and in most subsequent papers, the instantons are closed loops, which give probabilities integrated over particle momenta (and summed over spins).
We have developed an instanton formalism with open worldlines to obtain the momentum spectrum for Schwinger pair production in realistic 4D fields.
We have also shown how to use open worldlines for other strong-field processes such as nonlinear Compton emission of hard photons ($e^{-}\to e^{-}\gamma$), nonlinear Breit-Wheeler ($\gamma\to e^{+}e^{-}$) and trident ($e^{-}\to e^{-}e^{-}e^{+}$).

Speaker: Greger Torgrimsson (Umeå university)

14:30 → 15:15 Talk

Convener: Patrick Copinger (University of Plymouth)

14:30 Boundary conditions and proper-time contours for worldline path integrals

In standard uses of the worldline path integral formalism, Dirichlet or periodic boundary conditions are typically employed to calculate relevant quantities. However, when representing wave functions via path integrals, mixed boundary conditions emerge, where one end adheres to a Dirichlet or Neumann condition, while the other satisfies the opposite. Through straightforward examples from strong-field QED and Rindler spacetime, we illustrate how these boundary conditions lead to the corresponding wave functions. Furthermore, these examples reveal intriguing connections between proper-time contours and horizon-crossing.

Speaker: Karthik Rajeev

Karthik_Rajeev.pdf

15:15 → 15:45 Coffee Break

15:45 → 17:15 Discussions

Wednesday 26 February

09:15 → 10:00 Talk

Convener: Karthik Rajeev

09:15 Worldline approach for spinning bound binaries

We will discuss how to use the wordline formalism to compute scattering and bound observables for the classical two-body problem in general relativity, with particular emphasis on the case of Kerr black hole solutions. First, new classical Dirac brackets will be introduced to streamline the calculation of scattering observables for spinning binaries. Then, we will study the geodesic solution and higher order corrections in the framework of gravitational self-force theory, highlighting the importance of the resummation of the perturbative expansion. Finally, I will summarize the status of scattering-to-bound maps, which are crucial tools to extract relevant gauge-invariant bound observables for the inspiral regime of Kerr black holes binaries.

Speaker: Riccardo Gonzo (University of Edinburgh)

10:00 → 10:45 Talk

Convener: Karthik Rajeev

10:00 Gravitational Waves from Worldline Quantum Field Theory

The Worldline Quantum Field Theory (WQFT) formalism has proven itself a powerful tool for perturbatively calculating the physical observables involved in two-body gravitational scattering events — change in momentum, scattering angles, radiated energy and angular momentum. In this talk I will review the WQFT formalism and summarise this progress. In particular, I will discuss recent work on scattering spinning black holes using bosonic worldline oscillators, and our recent state-of-the-art calculation of 5PM (4-loop) scattering observables, which includes functions deriving from a Calabi-Yau threefold geometry.

Speaker: Gustav Mogull (Queen Mary University of London)

edinburgh25.pdf

10:45 → 11:15 Coffee Break

11:15 → 12:45 Discussions

13:45 → 14:15 Short Talk

Convener: Ivan Ahumada

13:45 Resummations and pair creation in the first quantised approach

The interaction of quantum fields with classical backgrounds gives rise to several interesting effects. For the study of the non-perturbative ones, the application of suitable resummation techniques is essential.

In this talk we will review recent advances in the development of appropriate resummation techniques, with special emphasis on those related to the first quantised approach. In particular, we will show how they relate to the effect of pair creation for a variety of backgrounds, including both an electromagnetic and gravitational one.

Speaker: Sebastian Franchino-Viñas (Università di Genova)

franchino_edinburgh_web.pdf

14:15 → 14:45 Short Talk

Convener: Ivan Ahumada

14:15 Effective Actions in a Supermanifold

Supergeometric Quantum Field Theories (SG-QFTs) are theories that go beyond the standard supersymmetric framework, since they allow for general scalar-fermion field transformations on the configuration space of a supermanifold, without requiring an equality between bosonic and fermionic degrees of freedom. After revisiting previous considerations, we extend them by calculating the one-loop effective action of minimal SG-QFTs that feature non-zero fermionic curvature in two and four spacetime dimensions. By employing an intuitive approach to the Schwinger–DeWitt heat-kernel technique and a novel field-space generalised Clifford algebra, we derive the ultra-violet structure of characteristic effective-field-theory (EFT) operators up to four spacetime derivatives that emerge at the one-loop order and are of physical interest. Upon minimising the impact of potential ambiguities due to the so-called multiplicative anomalies, we find that the EFT interactions resulting from the one-loop supergeometric effective action are manifestly diffeomorphically invariant in configuration space. The extension of our approach to evaluating higher-loops of the supergeometric quantum effective action is described. The emerging landscape of theoretical and phenomenological directions for further research of SG-QFTs is discussed.

Speaker: Viola Gattus (The University of Manchester)

SG_QEA.pdf

14:45 → 15:15 Coffee Break

15:15 → 16:45 Discussions

Thursday 27 February

09:15 → 10:00 Talk: Plenary Address

Convener: James Edwards (University of Plymouth)

09:15 Worldline approach to QED in external fields

The worldline formalism has been found particularly suitable for calculations in QED in external fields, including effective actions, amplitudes as well as Schwinger pair-creation rates. Here I will give a short summary of what has been achieved in this context, focussing mostly on constant and plane-wave fields.

Speaker: Christian Schubert (Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolas de Hidalgo)

10:00 → 10:45 Talk

Convener: Riccardo Gonzo (University of Edinburgh)

10:00 Classical worldlines from scattering amplitudes

The rapid advance in gravitational wave detectors has spurred renewed interest in the two-body problem in general relativity. Two perturbative approaches based on quantum field theory have emerged, one based on scattering amplitudes and the other based on worldlines. We argue that the two approaches are equivalent at an intimate level. By systematic algebraic manipulations through the Schwinger parametrization, the loop integrand in the Kosower-Maybe-O'Connell formalism based on wavepacket scattering becomes identical to the counterpart in worldline formalisms, as shown explicitly for a simple scalar model as well as electrodynamics at two loops. This makes manifest the cancellations of unphysical divergences in the classical limit and demonstrates the emergence of the classical worldline picture including the causality flow.

Speaker: Dr Mao Zeng (The University of Edinburgh)

talkFirstQuantizationWorkshop.pdf

10:45 → 11:15 Coffee Break

11:15 → 12:00 Talk

Convener: Riccardo Gonzo (University of Edinburgh)

11:15 Tadpole contribution to magnetic photon-graviton conversion

In this talk, I will provide a brief review of the reducible contributions
to QED amplitudes in a constant background field from the worldline
perspective. The focus will be on the missing piece in photon-graviton
conversion in a magnetic field. This process is typically studied at tree
level, but one-loop corrections involving scalars and spinors have also been
calculated. Unlike the tree-level process, the one-loop amplitude exhibits a dependence
on photon polarization, leading to dichroism. However, previous calculations
overlooked a tadpole contribution, which was historically assumed to vanish
in QED but was recently shown to have been incorrectly dismissed.
Here, we compute this missing diagram in closed form and demonstrate that it
does not contribute to dichroism.

Speaker: Naser Ahmadiniaz (Helmholtz-Zentrum Dresden - Rossendorf (HZDR))

Naser-Edinbrugh.pdf

12:00 → 13:15 Discussions

14:15 → 15:00 Talk

Convener: Anton Ilderton (UoE)

14:15 Flying focus, self-duality and scattering

Flying focus beams are exact solutions of the Maxwell equations with spatial focussing, a feature which is absent in plane waves. In the first instance, these flying focus solutions are complex-valued; unfortunately, taking the real part of this field results in background-coupled wave equations for particles interacting with the real background field that are complicated PDEs. In this talk, we'll discuss how keeping the original, complex flying focus solution enables remarkable analytic calculations. In particular, the complex-valued flying focus beam is a self-dual Maxwell field, and the hidden integrability associated with this fact makes it possible to solve background-coupled wave equations exactly in the ultrarelativistic (massless) regime. This enables analytic computation of non-linear Compton scattering, as well as multi-emission amplitudes in 'maximal helicity violating' configurations. These scattering amplitudes on the complex field can in turn be viewed as encoding depletion on the real-valued background.

Speaker: Tim Adamo (University of Edinburgh)

HCTP25.pdf

15:00 → 15:30 Coffee Break

15:30 → 16:15 Discussions

16:15 → 16:30 Closing Remarks

Conveners: Anton Ilderton (UoE), James Edwards (University of Plymouth)